478 



RICE 



ART. K 



and ri -\- dr). There is no change in the mass of the solid, but its 

 volume will change by an amount given by 



dvv = Andan + ^i2<iai2 • • • + Azzdas^. 



This result depends on the fact that if the constituents of the 

 determinant \a\, written above, are all altered by infinitesimal 

 amounts, dan, dan, etc., then the infinitesimal change in the 

 value of \a\ is equal to the expression on the right-hand side 

 of the equation just written. Now by equation [355] 



de = tdrj + Xx'dan + Xy'da 



12 



+ Zz'da. 



33, 



[400a] 



since for the postulated cube ev and riv are identical with « 

 and t]. Also from [388] 



dt = td-q + ridt — pdv — vdp + mdm, 



remembering that vv is identical with v. 

 Equating [400a] and [401] we obtain 



■qdt — vdp + mdni = Xx' dan + Xy da^ + . . 



+ Zz' dttss + pdv 

 = {Xx' + An p) dan + {Xy + An p) da^ + . . 

 + (Zz- + Azi p) dazz. 



[401] 



-. [404a] 



This is our form of equation [404]. If we then proceed to 

 equation [405] which holds for a fluid identical in substance 

 with the solid (so that we are dealing with fusion and solidifica- 

 tion) we arrive at our form of [406], viz., 



(vf — v) dp — {riF — 7]) dt = (Xx' -{- Anp) dan 

 + {Xy' + An p) dan . . . + {Zz' + Azz p) dazz. [406a] 

 In consequence we find that 



dp 

 dt 



Q 



[407] 



t{vF — v) 

 Let us recall that p is the fluid pressure on a pair of opposite 



